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Example 4.7.1.31. Let $(T, \leq )$ be a nonempty linearly ordered set. The following conditions are equivalent:

  • The cofinality $\mathrm{cf}(T)$ is a positive integer.

  • The cofinality $\mathrm{cf}(T)$ is equal to $1$.

  • The linearly ordered set $T$ contains a largest element.